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[Reprinted  from  the  Bulletin  of  the  Bureau  of  Standards,  Vol.  2,  No.  1.] 

Talbot's  Law  as  Applied  to  the 
Rotating  Sectored  Disk 


SUBMITTED   TO   THE   BOARD   OF   UNIVERSITY   STUDIES   OF 

THE  JOHNS  HOPKINS  UNIVERSITY,  IN  CONFORMITY 

WITH  THE  REQUIREMENTS  FOR  THE  DEGREE 

OF    DOCTOR    OF  PHILOSOPHY. 


BY 

EDWARD  P.  HYDE. 


BALTIMORE, 

1906. 


DEPARTMENT    OF    COMMERCE    AND    LABOR 

BUREAU     OF     STANDARDS 

S.  W.  STRATTON,  Director 


BY 


E.  P.  HYDE,  Assistant  Physicist 
\^ 

Bureau  of  Standards 


REPRINT  NO.  26 
(FROM  BULLETIN,  VOL.  2,  NO.  1,  BUREAU  OF  STANDARDS) 


WASHINGTON 

GOVERNMENT    PRINTING    OFFICE 
1906 


TALBOT'S  LAW  AS  APPLIED  TO  THE  ROTATING 
SECTORED  DISK. 


By  Edward  P.  Hyde. 


1.  Introduction. 

2.  Theoretical  Discussion. 

a.  Radiation  from  a  cylindrical  source. 

b.  Method  of  mean  distances. 

3.  Apparatus  and  Methods. 

a.  General  method. 

b.  Sources. 

c.  Disks. 

d.  Details  of  methods. 

White  light. 
Colored  light. 

4.  Experimental  Results. 

a.  Effect  of  speed. 

b.  Disks. 

c.  White  light. 

d.  Colored  light. 

5.  Conclusions. 


1.  INTRODUCTION. 

The  rotating  sectored  disk  is  one  of  the  most  valuable  adjuncts  in 
photometric  investigation,  and  yet  from  the  first  announcement  by 
Talbot1  of  the  law  governing  its  operation  until  the  present  time 
the  application  of  the  sectored  disk  has  been  limited  by  a  wide- 
spread doubt  of  the  general  truth  of  the  law  announced  by  Talbot. 
This  law  is  stated  by  Helmholtz  as  follows:2  "If  any  part  of  the 
retina  is  excited  with  intermittent  light,  recurring  periodically  and 

1Phil.  Mag.,  Ser.  3,  Vol.  5,  p.  321;  1834. 
3  Physiolog.  Optik,  II  Auflage,  p.  483. 


166189 


2  Bulletin  of  the  Bureati  of  Standards.  \.voi.  2,  NO.  i. 

t 
regularly  in  the  same  way,  and  if  the  period  is  sufficiently  short,  a 

continuous  impression  will  result,  which  is  the  same  as  that  which 
would  result  if  the  total  light  received  during  each  period  were  uni- 
formly distributed  throughout  the  whole  period." 

Talbot's  law  is  thus  a  statement  of  physiological  rather  than  of 
physical  phenomena,  and  depends  for  its  explanation  on  the  action 
of  the  eye.  Talbot  recognized  this  and  was  consequently  led  to 
state,  "  I  need  hardly  observe  that  it  would  be  illogical  to  assert  a 
priori  the  existence  of  this  law  of  optics,  however  simple  and  natural 
it  may  appear,  unless  we  were  perfectly  well  acquainted  with  the 
circumstances  which  accompany  the  action  of  light  upon  the  retina, 
which  is  very  far  from  being  the  case.  Its  proof  can  rest  on  experi- 
ment alone,  and  by  that  it  seems  to  be  most  satisfactorily  established." 

Many  experimenters  since  Talbot  have  investigated  the  law,  nota- 
bly Plateau,1  Helmholtz,2  Pick,3  Kleiner,4  Wiedemann  and  Messer- 
schmidt,5  and  more  recently  Ferry,6  and  Lummer  and  Brodhun.7 
Of  the  earlier  investigators  Plateau,  Helmholtz,  Kleiner,  and  Wiede- 
mann and  Messerschmidt  verified  the  law  within  their  range  of 
experimental  error,  which  was  always  several  per  cent.  Pick,  from 
theoretical  considerations  of  the  complex  action  of  the  eye  as  shown 
in  the  phenomena  known  as  "Anklingen"  and  "  Abklingen,"  con- 
cluded that  a  law  as  simple  as  that  of  Talbot  is  impossible.  He, 
moreover,  repeated  Plateau's  experiments  and  was  led  to  the  conclu- 
sion that  Talbot's  law  is  not  true  in  general,  but  that  with  more 
intense  illuminations  the  action  of  the  intermittent  light  is  stronger 
than  it  should  be  according  to  the  law,  and  that  perhaps  with  very 
weak  illumination  the  effect  is  reversed.  Aubert8  criticised  Pick's 
conclusions  on  the  ground  that  the  deviations  which  he  found  were 
of  the  same  order  of  magnitude  as  his  experimental  error,  and  that 
therefore  his  results  verified  the  law  to  within  the  limit  of  accuracy 
of  his  experiments. 

1  Pogg.  Annalen  der  Physik,  35,  p.  457;  1835. 

2  Physiolog.  Optik,  II  Auflage,  p.  483. 

3  Reichert's  u.  du  Bois-Reymond's  Archiv.,  p.  739;  1863. 

4  Pfliiger's  Archiv.  18,  p.  542;  1878. 
5\Vied.  Ann.  34,  p.  465;  1888. 
«Phys.  Rev.  1,  p.  338;  1893. 

7  Zs.  fiir  Instrumentenkunde,  16,  p.  299;  1896. 

8  Physiologic  der  Netzhaut,  p.  351. 


Hyde.}  The  Rotating  Sectored  Disk.  3 

Of  the  two  more  recent  investigations  Ferry  verified  the  law  for 
white  light,  but  found  quite  large  errors  when  the  light  transmitted 
through  the  rotating  sectored  disk  was  of  a  bluer  quality  than  that 
incident  on  the  other  side  of  the  photometer  screen.  His  method 
consisted  in  mounting  two  sources  of  light  on  the  photometer  bench, 
one  at  each  end,  and  interposing  in  the  path  of  the  rays  from  one 
source  a  rotating  sectored  disk  with  variable  openings.  The  disk 
\vas  mounted  on  a  movable  support  so  that  it  could  readily  be  intro- 
duced in  the  path  of  the  rays  and  quickly  removed  again  after  a 
reading  had  been  made. 

In  this  way,  using  as  sources  two  16  cp  incandescent  electric 
lamps  of  approximately  the  same  color,  he  found  the  law  to  be 
verified  for  all  openings  of  the  sector  down  to  a  total  angle  of  24°. 
Moreover,  as  the  voltage  on  the  lamps  was  changed  from  70  to  120 
volts,  provided  the  two  lamps  were  changed  together,  the  result  was 
the  same  as  before.  He  then  mounted  a  50  cp  incandescent  lamp 
at  the  disk  end  of  the  bar  and  a  16  cp  lamp  at  the  other  end,  and 
found  as  before  that  Talbot's  law  is  verified  if  the  two  lamps  are 
of  approximately  the  same  color.  If,  however,  the  50  cp  lamp  was 
burned  at  a  voltage  much  higher  than  the  normal,  or  if  a  piece  of 
slightly  tinted  blue  glass  was  interposed  in  the  path  of  the  rays 
intercepted  by  the  sectored  disk,  a  very  appreciable  deviation  from 
Talbot's  law  was  introduced  when  the  opening  of  the  disk  was 
less  than  180°,  the  deviation  increasing  as  the  opening  was  made 
smaller.  Using  successively  an  enclosed  arc  lamp  and  a  lime  light 
on  the  sectored  disk  side  of  the  photometer  and  an  incandescent 
lamp  on  the  other  side,  he  obtained  deviations  amounting  to  15  per 
cent  and  10  per  cent,  respectively,  at  24°,  the  deviation  in  each  case 
being  approximately  zero  when  the  opening  of  the  disk  was  greater 
than  1 80°.  In  all  cases  in  which  deviations  from  the  law  were 
found  the  disk  let  through  less  light  than  that  demanded  by  Tal- 
bot's law. 

As  a  result  of  his  observations  Ferry  concluded  that  although 
Talbot's  law  is  true  for  white  light,  "  with  mixed  light  containing 
elements  of  different  luminosity  shining  upon  the  retina,  a  rotating 
sectored  disk  will  appear  to  not  cut  off  all  the  elements  in  equal 
proportion,  but  will  intercept  most  strongly  the  elements  of  low 
luminosity."  Further,  "  with  any  given  light  the  error  introduced 


4  Bulletin  of  the  Bureau  of  Standards.  \yoi.2,  NO.  i. 

by  the  use  of  the  rotating  sectored  disk  increases  as  the  aperture  of 
the  disk  diminishes,"  although  "with  ordinary-  illuminants,  the 
error  is  negligible  when  the  total  aperture  of  the  disk  is  more  than 
one-half  the  entire  disk,  but  rapidly  increases  as  this  aperture  is 
diminished." 

Inasmuch  as  experiments  made  by  the  writer  yielded  results  quite 
different  from  those  of  Ferry,  it  seems  desirable  to  examine  care- 
fully his  experiments  and  results.  Unfortunately,  owing  to  lack  of 
detail  in  Ferry's  paper,  it  is  difficult  to  subject  these  to  a  searching 
criticism,  and  yet  there  are  several  points  to  which  it  may  be  well 
to  call  attention. 

First,  it  is  to  be  noticed  that  when  the  two  incandescent  lamps 
were  varied  simultaneously  from  70  to  120  volts — i.  e.,  over  quite  a 
large  range  of  color — no  error  was  observed,  but  that  when  one  lamp 
was  burned  at  a  voltage  somewhat  higher  than  normal  while  the 
other  was  kept  at  the  normal  voltage  a  relatively  large  error  was 
found.  The  question  immediately  arises:  What  would  have  been 
the  result  if  the  second  lamp  also  had  been  burned  at  a  voltage 
somewhat  higher  than  normal  ?  Since  there  is  nothing  in  the  paper 
to  indicate  the  normal  voltages  of  the  two  lamps,  which  were  varied 
from  70  to  1 20  volts,  we  are  at  a  loss  to  answer  the  question.  It  is 
probable,  however,  that  the  upper  limit  of  such  a  large  range  would 
represent  a  voltage  at  least  as  high,  if  not  higher,  than  the  normal. 
On  this  assumption  we  would  conclude  that  although  the  change  in 
color  produced  by  a  decrease  in  voltage  from  120  to  70  volts  is 
accompanied  by  no  error  in  Talbot's  law,  the  color  change  due  to  a 
rise  in  voltage  somewhat  above  the  normal  causes  a  relatively  large 
error  in  the  law  for  openings  of  small  angles.  In  other  words,  the 
color  corresponding  to  the  normal  voltage  is  a  critical  color. 

Since  this  is  quite  improbable,  we  are  led  to  conclude  that  the 
cause  of  the  error  when  the  lamp  at  the  disk  end  of  the  bar  was 
raised  to  a  voltage  somewhat  higher  than  the  normal,  while  the 
other  lamp  was  kept  at  the  normal  voltage,  is  to  be  found  in  the 
color  difference  which  existed  on  the  two  sides  of  the  screen. 
While  it  is  difficult  to  understand  why  the  color  of  one  side  should 
influence  the  effect  of  the  rotating  sector  on  light  from  the  other 
lamp,  it  is  to  be  noted  that  in  all  probability  a  different  form  of 
photometer  was  used  when  the  color  difference  existed,  and  this 


Hyde.]  The  Rotating  Sectored  Disk.  5 

might  perhaps  account  for  the  error.  Ferry  states  in  his  introduc- 
tion that  for  lights  of  the  same  color  a  Lummer-Brodhun  pho- 
tometer was  used,  but  that  when  a  considerable  color  difference 
existed  a  Bunsen  photometer  was  employed.  When  the  difference 
in  color  on  the  two  sides  was  small,  he  found  the  Nichols-Ritchie 
photometer  to  give  the  best  results.  In  describing  his  experiments 
he  does  not  state  explicitly,  however,  which  form  of  photometer  he 
used  in  each  case. 

Because  of  this  lack  of  definiteness  in  Ferry's  paper  it  seemed  very 
desirable  to  make  further  experiments  on  the  influence  of  color  on 
the  action  of  the  rotating  sectored  disk.  There  are  also  two  very 
definite  reasons  why  Ferry's  results  are  open  to  criticism.  First, 
since  the  absolute  illumination  of  the  photometer  screen  was  always 
much  greater  without  the  disk  than  with  it,  the  Purkinje  effect  would 
produce  errors  in  the  results  when  the  two  sources  differed  to  any 
extent  in  color.  Secondly,  the  inverse  square  law  applies  rigorously 
only  to  point  sources  and  can  not  be  assumed  a  priori  for  such  an 
extended  source  as  the  filament  of  an  incandescent  lamp,  particularly 


Fig.  1. — Lummer  and  Brodhun's  Arrangement. 

when  it  is  surrounded  by  the  reflecting  and  refracting  glass  bulb, 
which  alters  the  curvature  of  the  emitted  light  to  such  an  extent 
that  in  some  directions  sharp  images  of  the  filament  are  formed  sev- 
eral meters  away.  The  lime  light  and  the  enclosed  arc  lamp,  apart 
from  the  possible  errors  due  to  the  inapplicability  of  the  inverse 
square  law,  would  seem  to  be  unsuitable  for  accurate  work  because 
of  their  great  unsteadiness. 

The  most  satisfactory  work  that  has  been  done  on  Talbot's  law  is 
that  of  Lummer  and  Brodhun  at  the  Physikalisch-Technische  Reichs- 
anstalt.  These  investigators  first  verified  the  law  for  white  light 
down  to  50°  total  opening,  by  using  two  incandescent  electric  lamps, 
thus  far  being  merely  a  repetition  of  Ferry's  work.  Recognizing, 
however,  the. possible  error  due  to  the  inapplicability  of  the  inverse 
square  law,  they  modified  their  experiments  in  the  following  man- 
ner. Three  incandescent  lamps  were  mounted  on  the  photometer 
bench,  as  shown  in  Fig.  i.  Lamp  a  burned  continuously  but  lamp 


6  Bulletin  of  the  Bureau  of  Standards.  \yoi.z,  NO.  i. 

b  and  lamp  c  were  burned  successively,  and  the  current  through  each 
was  regulated  until  each  produced  approximately  the  same  illumina- 
tion of  the  screen.  They  were  then  both  burned  at  the  same  time,  the 
rotating  disk  with  a  total  opening  of  180°  was  placed  between  them 
and  the  photometer,  and  a  balance  was  obtained  by  moving  lamp  a. 
In  this  way,  since  the  distance  from  lamp  a  to  the  screen  remained 
approximately  constant,  errors  in  the  application  of  the  inverse 
square  law  entered  only  as  second  order  effects  and  were  hence  neg- 
ligible. In  a  similar  way  each  lamp  in  turn  was  burned  with  the 
disk  set  at  180°  total  opening,  and  then  both  were  burned  simultane- 
ously with  the  disk  set  at  90?  In  every  case  the  deviations  from 
the  law  were  found  to  be  of  the  same  magnitude  as  the  experimental 
error,  which  was  less  than  one-half  per  cent.  It  is  not  stated,  how- 
ever, how  far  the  process  was  carried,  except  that  it  was  not  extended 
to  very  small  angular  openings. 

Although  the  results  of  Lummer  and  Brodhun  are  conclusive  as 
far  as  they  go,  attention  should  be  called  to  the  fact  that  because 
the  observational  error  was  less  than  one-half  per  cent,  it  does  not 
necessarily  follow  that  Talbot's  law  was  verified  to  such  a  high 
accuracy  for  all  angular  openings  that  they  used.  Since  their 
method  of  observation  consisted  in  verifying  the  law  step  by  step, 
between  360°  and  180°,  180°  and  90°,  etc.,  the  error  between  360° 
and,  say,  22^°  would  be  distributed  over  four  intervals,  so  that 
though  the  error  within  each  interval  may  be  less  than  one-half  per 
cent  it  is  possible  that  an  error  of  i  or  2  per  cent  might  exist  between 
360°  and  22^°  without  being  detected.  This  fact,  together  with  a 
desire  to  check  Ferry's  results  for  colored  light,  led  the  writer  to 
make  the  experiments  described  in  the  following  pages. 

In  the  investigation  of  Talbot's  law  by  the  use  of  the  rotating 
sectored  disk  some  other  law  of  the  variation  of  the  intensity  of  illu- 
mination must  be  assumed.  Of  the  several  possible  ways  of  varying 
the  intensity  of  illumination  of  the  screen  the  method  of  varying  the 
distance  between  the  source  and  the  screen  is  the  simplest  and  most 
satisfactory,  but  presupposes  the  knowledge  of  the  law  of  variation 
of  the  intensity  of  illumination  with  the  distance  for  the  source  to 
be  used.  If  the  source  is  a  point  source  the  inverse  square  law  holds; 
if  the  source  is  not  a  point  source — and  no  actual  source  is  strictly 
a  point  source — it  must  either  be  shown  that  within  the  limits  of 
accuracy  of  the  experiments  the  deviations  from  the  inverse  square 


Hyde.} 


The  Rotating  Sectored  Disk. 


law  are  negligible  under  the  conditions  under  which  the  source  is  to 
be  used,  or  else  the  deviations  from  this  law  must  be  determined 
and  applied. 

The  source  to  be  used  must  not  only  have  the  law  of  variation  of 
intensity  of  illumination  with  distance  known,  but  must  also  be 
constant  and  intense.  The  incandescent  lamp  fulfills  the  last  two 
conditions,  but,  as  heretofore  pointed  out,  it  does  not  fulfill  the  first 
condition. 

It  occurred  to  the  writer  to  try  as  a  source  a  direct  current  Nernst 
glower  without  a  globe.  Although  the  only  one  of  the  above  con- 
ditions that  could  be  postulated  a  priori  was  the  intensity,  experi- 


Fig.  2. — Radiating  Cylinder. 

ment  showed  that  the  glower  remained  sufficiently  constant  under 
certain  conditions  which  could  be  readily  obtained,  and  the  follow- 
ing theoretical  considerations  led  to  the  conclusion  that  the  inverse- 
square  law  can  be  applied  to  the  Nernst  glower  to  within  negligible 
errors  if  the  glower  is  not  brought  closer  to  the  photometer  screen 
than  20  or  30  cm.  The  Nernst  glower  was  therefore  used  through 
the  experiments,  and  with  entire  satisfaction. 

2.  THEORETICAL  DISCUSSION. 

(a)  Radiation  from  a  Cylindrical  Source. — Let  us  assume  that  the 
Nernst  glower  is  a  radiating  circular  cylinder  of  radius  # ,  length  2  h, 


8  Bulletin  of  the  Bureau  of  Standards.  \_voi.  2,  NO.  i. 

and  uniform  specific  light  intensity  i.  The  problem  then  consists 
in  determining  the  law  of  variation  of  the  intensity  of  illumination 
with  the  distance  for  a  uniform  radiating  cylinder. 

Let  us  further  assume  Lambert's  cosine  law  for  the  radiating 
cylinder.  Although  this  law  holds  rigorously  for  black  bodies  only, 
the  resulting  error  in  the  comparison  of  illuminations  at  different 
distances  would  be  quite  small.  If,  then,  we  let  <£  (Fig.  2)  be  the 
angle  of  emission  for  any  element  of  surface  dS  of  the  radiating 
cylinder;  6  the  angle  of  incidence  of  any  ray  on  a  screen  at  P  placed 
at  right  angles  to  OP,  where  OP  lies  in  the  plane  perpendicular  to 
the  axis  of  the  cylinder  at  its  middle  point,  O;  r  the  distance  from 
the  element  dS  to  the  screen  at  P;  then  the  intensity  of  illumination 
of  the  screen  at  P  is 

C  Ci  cos  (f>  cos  6  d  S  /  N 

/=JJ-^ (I) 

taken  over  that  part  of  the  curved  surface  of  the  cylinder  convex 
toward  P. 

Expressing  all  the  quantities  involved  in  the  above  equation  in 
terms  of  the  two  cylindrical  coordinates  a  and  jy,  we  get  for  the 
intensity  of  illumination  at  P,  at  a  distance  /,  from  the  axis  of  the 
cylinder — 

C  f(l  cos  a— a)  (I— a  cos  a)  ,  x 

T=i  a  \  '  \  ~^>dady  (2) 

I   (a  4- 1  — 2atcosa4-y) 

•/  •/    \  '  s   / 

in  which  the  limits  of  y  are  (— ^,  +  h\  and  the  limits  of  a  are 

1#         ,  t#\ 

(—cos     y,  +  cos     j> 

The  integral1  of  the  above  expression  is 

/Z  I  '    —   d       '  tif  /    \ 

=  7«cos      f,_r,  ,  a  (3) 


where 


+*[<s+  0^  «*-•  ^ 


1  This  integral  was  obtained  by  Prof.  A.  S.  Chessin,  of  Washington  University,  to 
whom  the  writer  desires  to  express  his  indebtedness. 


Hyde.} 


The  Rotating  Sectored  Disk. 


It  only  remains  to  substitute  for  the  constants  a  and  h  in  the 
above  equation  the  numerical  values  pertaining  to  a  Nernst  glower 
and  then  to  compute  the  value  of  J  for  different  distances,  /.  Before 
doing  this,  however,  it  is  interesting  to  note,  in  passing,  the  form 
which  the  equation  assumes  when  we  make  h  approach  infinity. 
Under  this  condition  q  approaches  unity,  and  so  in  the  limit,  equa- 
tion (3)  becomes 

TT  i  a 

In  other  words,  the  intensity  of  illumination  due  to  an  infinitely 
long  uniformly  radiating  cylinder  varies  inversely  as  the  first  power 
of  the  distance  from  the  axis  of  the  cylinder,  a  result  which  also 
follows  from  purely  physical  considerations  of  the  normal  flow  of 
energy  across  coaxial  cylindrical  surfaces. 

Let  us  now  substitute  the  dimensions  of  the  Nernst  glower  in 
equation  (3),  compute  the  intensity  of  illumination  at  different 
distances,  /,  and  compare  the  relative  values  with  those  obtained  on 
.  the  assumption  of  the  inverse  square  law.  Two  sizes  of  glowers 
were  used  in  the  investigation,  88-watt  glowers  and  44-watt  glowers. 
The  dimensions  of  the  former  are  ^=7.5  mm,  a  —  0.6  mm.  Of  the 
latter,  /i  =  6  mm,  #  =  0.4  mm.  If,  then,  in  the  above  equation  we 
put  /i—io  mm  and  #  =  i  mm  we  shall  include  both  glowers,  and 

TABLE  I. 

Deviation  from  the  Inverse  Square  Law  of  the  Radiation  of  a  Cylinder  20  mm  long  and  1  mm  radius. 


Distances,  / 

J  (Direct  Evaluation) 

J  (Inverse  Square  Law) 

Deviation 

3000 

1.0000                       X/3000 

1.0000 

s\J  3000 

±0.00  % 

2000 

2.2500                           " 

2.2500 

II 

+0.00   " 

1000 

9.0045                           " 

9.0000 

M 

+0.05   " 

500 

3.6040X10                  " 

3.6000X10 

II 

+0.11   " 

200 

2.2545X102               " 

2.2500X102 

II 

+0.20   " 

100 

9.0081  X  10  2               " 

9.0000  X  10  2 

" 

+0.09   " 

80 

1.4049X103               "     * 

1.4062X103 

II 

-0.09   " 

50 

3.5593X103               " 

3.6000X103 

(1 

—1.13   " 

the  deviations  from  the  inverse  square  law  which  we  shall  find  will 
be  greater  than  those  incident  to  the  use  of  either  glower.     The 


io  Bulletin  of  the  Bureau  of  Standards.  \yoi.2,No.i. 

results  of  this  substitution  for  different  distances,  /,  are  shown  in 
Table  I  and  Fig.  3.  In  the  first  column  of  Table  I  are  given  the 
distances,  /,  expressed  in  millimeters,  for  which  the  values  of  J  were 
computed.  The  second  column  contains  the  ratios  of  the  intensities 
at  the  different  distances,  /,  to  that  at  /=  3000  mm,  as  obtained  by 
direct  substitution  in  equation  (3);  and  the  third  column  gives  the 
same  ratios  obtained  by  the  inverse  square  law.  The  percentage 
errors  are  shown  in  the  fourth  column,  in  which  (-)-)  means  that 
the  intensity  of  illumination  determined  by  direct  evaluation  of  the 
integral  of  equation  (3)  is  relatively  greater,  as  compared  with  the 
intensity  at  /—  3000  mm,  than  the  value  obtained  by  the  inverse 
square  law  from  the  intensity  at  /=  3000  mm.  This  is  shown  in 
Fig.  3,  in  which  abscissas  are  distances,  /,  and  ordinates  are  per- 


,,,+  0.2% 


u— 0. 1% 
5-0.2% 

DISTANCE   FROM  AXIS  OF  CYLINDER  IN  MM 


Fig.  3. — Deviation  of  Radiation  of  Cylinder  from  Inverse  Square  Law. 

centage  deviations  from  the  inverse  square  law,  as  deduced  from  the 
value  of  the  intensity  at  /=  3000  mm.  It  is  thus  seen  that  the  value 
of  J  between  /=  3000  mm  and  I—  90  mm  is  greater  (as  compared 
withy  at  7=3000  mm)  than  the  value  of  J  deduced  on  the  assump- 
tion of  the  inverse  square  law,  the  maximum  deviation  being  about 
+  0.2  per  cent.  At  distances  less  than  about  90  mm  the  intensity 
becomes  very  much  less  than  the  values  demanded  by  the  inverse 
square  law,  the  deviation  at  1=  50  mm  being  over  i  per  cent. 

Since  in  the  experiments  described  below  the  extreme  distances 
used  were  /=  3000  mm  and  1=  500  mm  the  maximum  error  on  the 
assumption  of  the  inverse  square  law  for  the  Nernst  is  approximately 
o.i  per  cent,  which  is  entirely  negligible.  Moreover,  the  errors 
given  in  Table  I  and  Fig.  3  were  deduced  for  a  cylinder  having  the 


Hyde.']  The  Rotating  Sectored  Disk.  1 1 

dimensions  h— 10  mm,  a  =  i  mm,  which  are  somewhat  greater  than 
the  dimensions  of  an  88-watt  Nernst  glower,  and  much  greater  than 
the  dimensions  of  a  44-watt  glower.     Hence  the  true  errors  for  the  - 
Nernsts  are  probably  less  than  those  given  in  the  table. 

It  should  be  stated  that  the  above  theory  was  based  on  the  assump- 
tion of  a  true  circular  cylinder  with  constant  specific  light  intensity,  i. 
The  Nernst  glower  does  not  fulfill  either  of  these  conditions  rigor- 
ously. It  frequently  becomes  warped  after  burning  for  some  hours, 
and  direct  experiment  reveals  the  fact  that  the  intensity,  z,  is  differ- 
ent at  different  parts  of  the  filament.  These  deviations  probably 
remain  constant,  however,  during  a  series  of  experiments,  and  so 
only  introduce  differential  errors  in  the  relative  intensities  of  illumi- 
nation at  different  distances. 

(b)  Method  of  Mean  Distances. — In  the  above  investigation  /  was 
defined  to  be  the  distance  from  the  center  of  the  cylinder  to  the 
photometer  screen,  the  axis  of  the  cylinder  being  parallel  to  the 
screen,  and  the  centers  of  both  cylinder  and  screen  lying  in  the  same 
plane  perpendicular  to  the  axis  of  the  cylinder.  In  the  experimental 
method  employed  it  was  found  difficult  to  measure  this  distance 
directly  by  the  use  of  the  scale  on  the  photometer  bar.  The  glower 
was  therefore  mounted  in  a  horizontal  position  in  a  socket  that  could 
be  turned  about  a  vertical  axis  through  its  center.  The  position  of 
the  axis  of  rotation  on  the  bar  was  shown  by  an  index  attached  to 
the  carriage  on  which  the  socket  was  mounted,  so  that  distances 
between  the  axis  of  rotation  and  the  photometer  could  be  read  off 
the  scale  on  the  bar.  The  center  of  the  glower  was  now  placed 
approximately  in  the  axis  of  rotation,  and  readings  were  made  first 
with  one  side  of  the  glower,  [designated  (+)]  and  then  with  the 
other  side  of  the  glower  [designated  (  — )  ]  turned  toward  the  photo- 
meter. In  each  case  the  distance  was  measured  to  the  axis  of  rota- 
tion and  the  mean  of  the  two  readings  taken.  This  mean  distance 
was  the  distance  used  in  the  comparison  of  intensities  of  illumina- 
tion, and  it  must  hence  be  shown  that  the  square  of  the  ratio  of  one 
mean  distance,  x,  to  another  mean  distance,  x' ,  gives  the  true  value 
of  the  ratio  of  the  two  corresponding  illuminations,  J  and  J' . 

Before  proceeding  to  this  let  us  consider  a  different  way  of  inter- 
preting the  deviations  of  the  law  of  radiation  of  the  cylinder  from 
the  inverse  square  law.  Since  for  all  distances  greater  than  /—  90 


12 


Bulletin  of  the  Btireau  of  Standards. 


[  Vol.  2.  No.  i. 


mm  the  intensity  of  illumination  compared  with  the  intensity  at 
1=  3000  mm  is  slightly  greater  than  that  for  a  point  source,  we  may 
consider  the  cylinder  as  a  point  source,  the  effective  center  of  radia- 
tion of  which  is  at  the  center  of  the  cylinder  for  /=  3000  mm,  but 
for  distances  between  7=3000  mm  and  7=90 
mm  it  is  displaced  a  variable  small  amount 
toward  the  photometer  screen.  Hence,  as  the 
deviations  from  the  inverse  square  law  are 
very  small  for  all  distances  used  in  the  experi- 
ments, we  can  take  the  percentage  error  in 
distance  to  be  one-half  the  percentage  error  in 
intensity  of  illumination.  If,  therefore,  we 
take  one-half  the  ordinates  of  Fig.  3  we  obtain 
the  percentage  errors  in  the  effective  distances. 
In  this  way  we  can  determine  for  any  distance 
the  displacement,  c,  of  the  effective  center  of 
radiation  from  the  geometrical  center  of  the 
cylinder. 

We  will  suppose  now  that  the  geometrical 
center  of  the  cylinder  is  at  a  distance,  a,  from 
the  axis  of  the  socket  (Fig.  4).  Suppose 
further  that  the  photometer  screen  has  an 
intensity  of  illumination,  y,  the  distance  from  the  axis  of  the  socket 
to  the  screen  being  xl  when  the  (+)  side  of  the  Nernst  is  turned 
toward  the  screen,  and  x^  when  the  (— )  side  is  turned  in  that 
direction.  If  now  1^  and  72  are  the  effective  intensities  of  the  (+) 
and  (— )  sides  of  the  Nernst,  respectively,  considered  as  a  point 
source, 

J—f*,.    „ AS^f-v    _!_/» r\*  (5) 


Fig.  4. — Displacement  of 
Axis  of  Cylinder  from  Axis 
of  Socket. 


—  a— 


•O2 


In  a  similar  way  the  equation  corresponding  to  an  illumination, 
/'  is 

Tl  _                       ?\                           .   _                      ^  (£\ 

J       ~~(~l „ J\*~~(<r    '_!_/» s-'\Z  ^      ' 


Hence  the  true  ratio  of  J  to  J'  is 


x—a—c 


-C 


—  c 


(7) 


Hyde.}  The  Rotating  Sectored  Disk.  13 

which,  by  composition,  becomes 

- a 


(8) 

Or,  if  we  put 

X  -4-X  X  '  -\-  K  ' 

1    I    •*•  /        •*'l       1^  •*<  /     \ 

**-4J-tl*'= — —  (9) 


X         X  XX 


to  within  negligibly  small  quantities.  From  this  equation,  or  better 
from  equation  (10),  it  follows  that  for  a  true  point  source  at  the  cen- 
ter of  the  cylinder  the  ratio  of  the  intensities  obtained  by  taking  the 
mean  distances  x  and  x'  is  the  same  as  that  obtained  from  the  actual 
distances  x^  —  a  and  x\  —  a,  or  x^-\-a  and  xz'-\-a,  since  for  a  true 
point  source  c=c'=o  and  from  equations  (7)  and  (10) 

(12) 


In  the  actual  case  of  the  cylinder,  c  and  c1  have  very  small  values, 

as  pointed  out  above.     In  fact  since  —  Xioo  is  the  percentage  dis- 

x 

"ZC 

tance  correction,  and  —  x  100  is  the  percentage  deviation  of  the 

2,C  I 

intensity  from  the  inverse  square  law,  it  follows  that  —  is of  the 

x       100 

ordinate  of  the  curve  of  Fig.  3  expressed  as  a  decimal  fraction,  or  is 
equal  to  the  ordinate  of  the  curve  expressed  in  per  cent.  Since  the 
greatest  range  of  distance  used  was  between  V  =  \x'  —  a]  =  3000  mm 


14  Bulletin  of  the  Bureau  of  Standards.  [MI.  2,  NO.  /. 

and  /=  [x—a~\  =500  mm  we  see  from  the  curve  of  Fig.  3  that  c'  =  o 
and  c—  H-O.II  per  cent,  so  that  [eq.  (n)] 


/=  (1-0+0.11%)  (13) 

in  which  the  correction  is  negligible. 

Hence  the  method  employed  of  taking  the  mean  of  the  (+)  and 
(—  )  readings  gives  absolutely  true  results  for  a  point  source,  and 
for  a  cylinder  the  errors  are  only  those  incident  to  the  deviation 
from  the  inverse-square  law  of  the  radiation  of  the  cylinder. 

3.  APPARATUS  AND  METHODS. 

(a)  General  Method.  —  The  photometer  bench  on  which  the 
measurements  were  made  is  a  Reichsanstalt  precision  photometer 
bench  250  cm  long,  supplied  with  a  Lummer-Brodhun  contrast 
screen.  In  the  experiments  with  disks  of  small  opening  it  was 
necessary  to  use  greater  distances  than  could  be  obtained  on  the 
250  cm  bar.  In  these  cases  an  extension  was  fitted  to  one  end  of 
the  bench,  increasing  its  length  by  about  175  cm.  In  all  the 
experiments  except  those  in  which  there  was  a  decided  color  differ- 
ence the  contrast  principle  was  used  but  in  the  cases  of  great  color 
difference  the  absorption  strips  producing  the  contrast  were  removed 
and  the  setting  was  made  for  a  match. 

Throughout  the  experiments  the  substitution  method  was  em- 
ployed. Thus  the  source  at  the  right  end  of  the  bar  was  merely 
used  as  a  comparison  lamp.1  The  carriage  on  which  it  was  mounted 
was  connected  rigidly  by  means  of  adjustable  links  to  the  carriage 
supporting  the  photometer  screen  and  at  a  suitable  distance  to  pro- 
duce the  desired  illumination  of  the  screen.  The  comparison  lamp 
thus  moved  with  the  screen,  remaining  at  a  constant  distance  from 
it,  except  in  so  far  as  slight  irregularities  in  the  ways  produced 
small  variations  in  the  distance,  depending  upon  the  positions  of 
the  carriages  on  the  bar.  These  eccentricities  were  carefully  studied 
for  all  positions  of  both  carriages  on  the  bar  and  the  results  were 
tabulated,  so  that  the  variations  in  the  distance  between  the  com- 
parison lamp  and  the  screen,  as  the  latter  was  moved  back  and  forth 

1  Hereafter  the  lamp  on  the  right  will  be  referred  to  as  the  "comparison  lamp," 
in  distinction  from  the  '  '  test  lamp  '  '  on  the  left. 


Hyde. 


The  Rotating  Sectored  Disk. 


on  the  bar,  could  be  determined  directly.  Since,  however,  in  nearly 
every  experiment  the  position  of  the  photometer  was  approximately 
the  same  with  the  sectored  disk  stationary  and  rotating,  and  since 
regions  of  the  bar  were  selected  which  were  approximately  true,  in 
general  no  correction  was  necessary  for  the  distance  between  the 
comparison  lamp  and  the  screen.  Hence  the  illumination  on  the 
right  side  of  the  screen  remained  constant  to  within  the  variations 
of  the  comparison  source  itself. 

On  the  left  side  of  the  photometer  the  test  Nernst  and  the  sec- 
tored disk  were  mounted.     Fig.  5  is  a  diagrammatic  sketch  of  the 


D 

N 

C             S 

B  A 
P 

jv 

(eg 

aa 

r~\~] 

^) 

nh 

tef 

! 

Fig.  5. — Diagrammatic  Sketch  of  Photometer  Bench. 

general  arrangement,  in  which  A,  B,  C,  and  D  are  diaphragms 
covered  with  black  velvet,  which  were  always  so  arranged 
that  no  stray  light  could  reach  the  photometer  screen  except  by 
reflection  from  the  black  velvet  at  an  angle  approximately  equal  to 
90?  The  magnitude  of  this  stray  light,  when  the 
walls  of  the  room  were  white  and  were  rather 
strongly  illuminated,  was  found  by  a  previous 
investigation1  to  be  entirely  negligible.  M  is  a 
small  spherical  motor,  which  carries  on  its  shaft  the 
sectored  disk  >S.  NN  are  the  two  sources  and  P  is 
the  photometer  screen. 

(b)  Sources. — Direct  current  Nernst  glowers  were 
used  throughout  the  investigation  for  the  test  source 
at  the  disk  end  of  the  bar,  and  in  most  of  the  meas- 
urements a  glower  was  used  for  the  comparison 
lamp.  When  the  effect  of  color  difference  was  in- 
vestigated an  incandescent  lamp  at  low  voltage  was 
used  for  a  comparison  lamp,  and  in  some  few  experiments  on  colored 
light  an  incandescent  lamp  was  substituted  for  the  comparison 
Nernst.  As  stated  above,  the  glowers  were  burned  without  any 
globes  around  them,  since  reflection,  refraction,  and  diffusion  of  the 
light  by  the  globe  might  produce  serious  errors.  Moreover  the 


Fig.  6. — Nernst 
Glower  Mounted  on 
Extension  Plug: 


1  Bureau  of  Standards  Bulletin  No.  3,  p.  417. 
24353— No.  I— 06 2 


1 6  Btilletin  of  the  Bureau  of  Standards.  \_voi.  2,  NO.  i. 

glowers  were  not  provided  with  the  customary  ballast  resistance. 
They  were  mounted  on  extension  plugs,  as  shown  in  Fig.  6,  and  were 
operated  with  constant  current  on  a  storage-battery  circuit  of  250 
volts,  of  which  approximately  150  volts  was  taken  up  in  rheostats. 
This  series  resistance  took  the  place  of  the  customary  ballast  resist- 
ance and  served  to  keep  the  current  approximately  constant. 

The  electrical  measurements  were  made  in  terms  of  a  Weston 
standard  cell  by  means  of  a  potentiometer.  Thus,  the  current  was 
measured  by  the  difference  in  potential  across  a  standard  resistance 
and  the  voltage  was  obtained  by  the  use  of  a  100,000  ohm  multiplier. 
The  original  plan  was  to  leave  the  Nernst  glowers  entirely  uncov- 
ered, but  it  was  found  that  due  to  air  currents  the  resistance  of  the 
glowers  changed  continually,  so  that  it  was  impossible  to  maintain 
the  current  in  the  glowers  constant,  and  the  fluctuations  in  the  volt- 
age were  so  great  as  to  preclude  the  possibility 
of  measurement  closer  than  to  several  tenths 
of  i  per  cent.  Moreover,  the  effect  of  the 
rotating  disk  in  the  neighborhood  of  the 
Nernst  was  evident  both  in  the  current  and  in 
the  voltage.  I  was  thus  led  to  try  the  effect 
of  partially  surrounding  the  Nernsts  with 

hoods.     To  this  end  two  pieces  of  brass  tub- 
Fig.  7. -Horizontal  Section      •  Qm  j  and  T     cm  diameter  were  each 
of  Hood  through  Opening.                                  .  / 

provided   with    a  rectangular  opening   i    cm 

high  and  5  cm  wide  at  a  distance  of  28  cm  from  one  end  of  the 
tube,  so  as  to  be  opposite  the  Nernst  when  placed  on  the  base  of 
the  carriage  on  which  the  Nernst  was  mounted.  Each  of  these 
hoods  was  provided  with  a  loosely  fitting  piece  of  sheet  brass  for  a 
cover  and  was  painted  a  dead  black.  Lest  any  stray  light  might 
be  reflected  into  the  photometer  at  approximately  grazing  incidence 
from  the  outside  of  the  tube,  a  sheet  of  brass  25  cm  long  and  15  cm 
wide  was  covered  with  black  velvet  and  fastened  to  the  front  of  the 
hood  with  the  black  velvet  turned  toward  the  screen.  This  dia- 
phragm was  provided  with  a  rectangular  opening  to  correspond 
with  the  opening  in  the  hood,  as  shown  in  Fig.  7,  which  is  a  hori- 
zontal section  in  the  plane  of  the  opening.  That  part  of  the  inside 
of  the  tube  which  was  behind  the  Nernst  was  also  covered  with 
black  velvet  in  order  to  prevent  any  possible  reflection  from  the 
painted  metal  surface. 


Fig.  8. — Sectored  Disk  Mounted  on  Photometer  Bar. 


Hyde.]  The  Rotating  Sectored  Disk.  1 7 

Under  these  hoods  the  Nernsts  operated  almost  as  steadily  as 
incandescent  lamps.  The  current  could  be  maintained  constant  to 
within  i  or  2  parts  in  10,000,  and  the  voltage  could  usually  be 
measured  to  the  same  accuracy.  Moreover,  the  luminous  intensity 
remained  constant  to  within  the  limit  of  observational  error,  and 
the  sectored  disk  in  the  neighborhood  of  the  Nernst  seemed  to  have 
no  appreciable  effect  on  its  voltage  at  constant  current,  which 
affords  a  quite  sensitive  means  of  determining  slight  variation  in 
the  temperature  of  the  Nernst.  It  was  for  this  reason  that  voltage 
measurements  were  made  with  every  series  of  observations. 

One  peculiar  voltage  effect  was  noticed  which  occurred  at  times 
both  when  the  disk  was  stationary  and  when  it  was  rotating.  The 
voltage  would  suddenly  change  over  several  tenths  of  a  volt  and 
then  gradually  creep  back.  As  this  change  was  usually  accompa- 
nied by  no  perceptible  variation  in  the  luminous  intensity,  if  the 
current  was  maintained  constant,  and  as  it  seemed  to  occur  more 
frequently  after  the  Nernsts  had  burned  for  many  hours,  it  seemed 
probable  that  it  was  due  to  the  cracking  of  the  terminals  of  the 
filament  and  a  consequent  redistribution  of  the  current  at  the  ter- 
minals. This  hypothesis  seemed  to  be  borne  out  by  the  fact  that 
in  all  old  Nernsts  the  positive  ends  show  large  and  deep  cracks. 

At  first  the  presence  of  these  sudden  changes  in  the  voltage 
caused  doubt  as  to  the  accuracy  of  the  results.  They  repeatedly 
occurred  both  while  the  disk  was  stationary  and  while  rotating,  and 
could  not  be  detected  at  the  photometer,  although  every  other  con- 
dition was  maintained  constant.  I  was  therefore  led  to  disregard 
them,  particularly  as  the  results  obtained  in  sets  in  which  there  was 
no  trace  of  such  an  effect  agreed  with  those  obtained  in  sets  in 
which  the  effect  was  plainly  noticeable. 

Having  shown  that  the  Nernst  could  be  depended  upon  for  its 
constancy,  it  remained  to  find  some  convenient  way  of  determin- 
ing the  distance  between  the  center  of  the  test  Nernst  and  the  pho- 
tometer screen.  The  test  Nernst  (as  distinguished  from  the  com- 
parison Nernst)  mounted  on  an  extension  plug,  was  screwed  into 
the  socket  of  a  horizontal  rotator  with  the  driving  shaft  removed. 
But  although  the  distance  from  the  axis  of  the  rotator  to  the  near 
surface  of  the  plaster  of  Paris  screen  in  the  photometer-head  was 


i8  Bulletin  of  the  Bureau  of  Standards.  [  vol.  2,  NO.  /. 

known  for  every  position  of  the  rotator  and  of  the  photometer-head, 
as  the  result  of  a  direct  calibration  of  the  scale  on  the  bar,  the  dis- 
tance of  the  center  of  the  Nernst  from  the  axis  of  the  rotator 
varied  slightly  from  time  to  time,  due  to  bending  of  the  terminal 
wires  of  the  Nernst  on  heating,  etc.  Hence,  after  each  series  of 
measurements  it  was  necessary  to  re-determine  the  distance.  It 
therefore  occurred  to  the  writer  to  use  the  method  described  briefly 
in  the  above  theory.  A  double  pointer  was  attached  to  the  rotator, 
and  by  means  of  a  corresponding  pointer  attached  to  the  carriage 
the  Nernst  could  be  turned  through  180?  The  mean  of  the  (+) 
and  (— )  readings  as  described  above  was  taken  in  each  case. 

(c)  Disks. — The  rotating  sectored  disk  is  shown  in  Fig.  8.  The 
rotating  device  consisted  of  a  small  spherical  direct  current  fan 
motor,  9  cm  in  diameter,  mounted  on  a  base  clamped  to  the  ways. 
In  the  figure  the  motor  and  disk  are  turned  slightly  with  reference 
to  the  base,  so  as  to  be  seen  better.  The  distance  of  the  motor 
above  the  ways  could  be  adjusted  by  means  of  the  telescoping 
tubes  which  formed  the  column  on  which  the  motor  was  mounted. 
The  frame  of  the  motor  was  japanned.  In  order  to  prevent  light 
from  being  reflected  into  the  photometer-head  from  the  smooth  sur- 
face of  the  motor,  the  top  of  the  motor  was  at  first  covered  with 
black  velvet,  but  since  the  light  was  incident  on  this  at  nearly  graz- 
ing incidence  it  was  thought  better  to  substitute  a  small  metal  screen 
placed  normal  to  the  direction  of  the  rays.  This  was  accomplished 
by  separating  the  two  halves  of  the  spherical  shell  of  the  motor  and 
inserting  a  blackened  piece  of  thin  sheet  aluminum  cut  to  fit.  This 
is  shown  in  the  figure. 

The  sectored  disks  were  mounted  directly  on  the  shaft  of  the 
motor  and  the  height  of  the  motor  was  adjusted  so  that  the  sector 
cut  the  beam  of  light  normally,  the  central  ray  of  the  beam  lying 
in  the  same  vertical  plane  as  the  shaft  of  the  motor.  Instead  of  the 
customary  method  of  using  a  graduated  variable  sectored  disk,  it 
was  decided  to  use  separate  disks  for  the  different  angular  openings. 
This  was  decided  upon  partly  because  four  such  disks  were  at  hand 
and  partly  because  there  was  less  chance  for  error  in  the  calibration 
of  the  opening.  The  original  four  disks  were  made  of  aluminum 
about  1.5  mm  thick,  and  each  contained  six  open  and  six  solid  sec- 
tors equally  spaced.  The  total  angular  openings  (which  will  here- 


Hyde.] 


The  Rotating  Sectored  Disk, 


after  always  be  meant  when  reference  is  made  to  the  opening  of  a 
disk  unless  it  is  stated  otherwise)  were  288°  (6x  48°),  270°  (6x  45°), 
240°  (6x40°),  and  180°  (6x30°).  Subsequently  the  following 
disks  were  added:  One  steel  disk,  1.5  mm  thick,  with  total  opening 
of  60°  in  three  sectors  of  20°  each;  two  hard  brass  disks,  1.5  mm 
thick,  with  total  openings  of  210°  in  six  sectors  of  35°  each,  and 
30°  in  six  sectors  of  5°  each. 

All  of  the  disks  were  approximately  30  cm  in  diameter,  and  had 
the  same  general  form  as  that  shown  in  Fig.  8.  They  were  all 
painted  dead  black,  and  the  last  two  disks  (210°  and  30°)  had  the 
edges  of  the  sectors  beveled  so  as  to  prevent  reflection  from  them. 

With  these  seven  disks  the  law 
could  be  tested  at  seven  points, 
ranging  irregularly  from  30°  to 
288?  In  order  to  obtain  more 
points  of  the  curve  it  was  decided 
to  cover  some  of  the  openings 
of  the  disks  with  thin  pieces  of 
blackened  aluminum  clamped  over 
the  openings  (Fig.  9).  The  covers 
were  always  placed  symmetrically, 
so  that  with  a  disk  of  six  open 
sectors  it  was  possible  to  obtain 
either  one-half  the  total  opening 
by  covering  the  alternate  sectors, 
or  to  obtain  one-third  the  total 

opening  by  covering  all  but  two  opposite  sectors.  Moreover,  by 
changing  the  covers  it  was  possible  to  obtain  the  same  opening  in 
different  ways,  i.  e.,  by  using  different  sectors  of  the  same  disk. 

By  this  method  the  following  total  openings  were  obtained:  10°, 
15°,  30°,  from  the  30°  disk;  60°  from  the  60°  disk,  and  also  from 
the  1 80°  disk;  90°  from  the  180°  disk  and  also  from  the  2 70°  disk; 
120°  from  the  240°  disk;  144°  from  the  288°  disk;  180°,  210°, 
240°,  270°,  and  288°  from  the  respective  disks. 

The  disks  were  all  carefully  calibrated  on  a  circular  dividing 
engine.  The  opening  of  each  sector  of  each  disk  was  measured  at 
seven  successive  radial  distances  0.5  cm  apart,  over  a  range  of  3 
cm,  since  3  cm  was  approximately  the  maximum  height  of  the  beam 


Fig.  9. — Sectored  Disk  with  Three  Openings 
Covered. 


2O  Bulletin  of  the  Bureau  of  Standards.  \_voi.  2,  NO.  i. 

at  the  point  where  it  was  intercepted  by  the  disk.  The  mean  of  the 
seven  readings  was  taken  as  the  opening  of  the  sector  and  the 
height  of  the  disk  was  always  so  adjusted  that  the  line  from  the 
center  of  the  Nernst  to  the  center  of  the  photometer  screen  inter- 
cepted the  disk  at  the  middle  point  of  the  region  over  which  it  had 
been  calibrated.  The  average  deviation  for  different  radial  dis- 
tances from  the  mean  value  for  any  combination  of  sectors  that  was 
ever  used  was  always  under  o.i  per  cent,  but  owing  to  difficulties  in 
setting  on  the  edges,  the  total  opening  was  perhaps  not  known  to 
an  accuracy  much  better  than  o.i  per  cent.  The  values  of  the  dif- 
ferent sectors  of  the  various  disks  are  given  in  the  "  Experimental 
Results." 

The  sectored  disk  in  all  cases,  with  one  or  two  exceptions  which 
will  be  noted  later,  was  placed  between  diaphragms  B  and  C  (Fig.  5) 
and  as  close  to  B  as  possible.  This  diaphragm  had  a  circular  aper- 
ture of  10  cm  and  hence  screened  the  motor  (except  the  upper  part) 
and  its  support  from  the  photometer  screen.  The  distance  between 
the  disk  and  the  photometer  screen  ranged  from  20  to  25  cm. 
Moreover,  the  sectored  disk  was  always  left  in  position  with  the 
open  sector  in  the  path  of  the  light  for  readings  intended  to  give  the 
direct  intensity,  except  when  the  30°  disk  was  used.  The  5°  sec- 
tors of  this  disk  were  too  narrow  to  permit  the  beam  to  pass. 
Measurements  made  with  the  larger  disks  removed,  however,  failed 
to  show  any  effect  of  the  stationary  disks. 

The  complete  arrangement,  except  the  extension  ways,  is  shown 
in  Fig.  10  which  was  made  from  a  photograph.  The  hood  was 
removed  from  the  comparison  Nernst  and  is  shown  standing  on  the 
table. 

(d)  Details  of  Methods —  White  Light. — The  method  of  conduct- 
ing the  experiments  was  as  follows:  Two  seasoned  Nernst  glowers 
were  mounted  in  the  two  sockets  and  the  test  Nernst  was  adjusted 
so  that  its  center  was  at  the  proper  height,  coinciding  very  nearly 
with  the  axis  of  the  rotator,  and  the  direction  of  its  axis  was  perpen- 
dicular to  the  line  joining  its  center  to  that  of  the  photometer  screen. 
The  two  Nernsts  were  then  brought  to  incandescence  and  allowed 
to  burn  about  an  hour.  The  test  Nernst  was  placed  at  some  definite 
position  and  the  connecting  links  between  the  photometer  screen 
and  the  comparison  Nernst  were  adjusted  until  the  balance  came  at 


ffyde.}  The  Rotating- Sectored  Disk.  21 

a  desirable  part  of  the  bar.  While  one  observer  maintained  the 
currents  constant  the  other  observer  made  the  photometric  settings. 
First,  with  the  disk  stationary,  a  series  of  three  or  more  readings 
was  made  with  the  Nernst  in  the  (+)  position,  then  a  second  series 
with  the  Nernst  in  the  (  — )  position,  and  then  two  more  series,  one 
(-)-)  and  the  other  (— ),  making  in  all  four  series  of  measurements 
with  the  disk  stationary.  The  sectored  disk  was  then  set  rotating 
and  the  test  Nernst  was  moved  in  nearer  to  the  photometer  screen 
to  some  position  such  that  the  balance  came  at  about  the  same  posi- 
tion on  the  photometer  bar  as  before.  The  carriage  holding  the  test 
Nernst  was  then  clamped  to  the  ways,  and  kept  at  this  fixed  position 
while  the  settings  for  a  balance  were  made.  As  explained  before, 
the  settings  were  made  by  moving  the  photometer  screen  and  com- 
parison Nernst,  which  moved  as  a  single  system  remaining  at  a 
constant  fixed  distance  apart  during  the  entire  experiment.  Four 
series  of  three  readings  each  were  then  made  as  with  the  disk 
stationary.  This  process  of  alternate  stationary  and  rotating  meas- 
urements was  continued  until  three  groups  of  stationary  readings, 
and  two  groups  of  rotating  readings  had  been  made,  making  a  total 
of  twelve  series  of  stationary  readings,  six  (-(-)  and  six  (  — ),  and 
eight  series  of  rotating  readings,  four  (+)  and  four  (— ).  The  square 
of  the  ratio  of  the  mean  distance  between  the  photometer  screen  and 
the  axis  of  the  rotator,  when  the  disk  was  rotating,  to  the  mean 
distance  when  the  disk  was  stationary,  was  taken  as  the  effective 
ratio  of  the  light  transmitted  by  the  disk  to  that  incident  on  it. 
The  comparison  of  this  ratio  with  the  ratio  of  the  angular  opening 
of  the  disk  to  360°  gave  the  deviation  from  the  law  for  the  disk 
used. 

This  method  was  used  for  all  the  disks  except  in  some  few  sets 
near  the  end  of  the  investigation  in  which  only  three  groups  of 
readings  instead  of  five  were  made.  In  all  cases  after  each  series  of 
three  readings  the  voltages  on  the  two  Nernsts  were  measured  and 
recorded. 

Colored  Light. — In  the  measurements  with  colored  light  the 
method  was  exactly  the  same  as  that  used  for  white  light  except 
that  a  piece  of  colored  glass  was  introduced  into  the  eyepiece 
of  the  photometer.  Red,  green,  and  blue  glasses  were  used  and 
measurements  were  made  on  three  disks,  the  240°  disk,  the  60°  disk, 


22  Bulletin  of  the  Bureau  of  Standards,  \_voi.  2.  NO.  i. 

and  the  15°  disk.  The  colored  glasses  used  were  not  monochro- 
matic, but  since  to  the  eye  the  light  appeared  distinctly  red,  or  green, 
or  blue,  as  the  case  may  be,  any  appreciable  error  due  to  one  of  the 
colors  would  probably  not  be  modified  greatly  by  the  admixture  of 
relatively  small  quantities  of  light  of  another  color. 

4.  EXPERIMENTAL  RESULTS.1 

(a)  Effect  of  Speed. — Before  beginning  the  investigation  of  Tal- 
bot's  law,  the  effect  of  the  speed  of  rotation  of  the  disk  on  the  illu- 
mination of  the  screen  was  tested.     Since  numerous  investigators 
have  found  that  the  speed  of  the  disk  has  no  effect  on  the  apparent 
illumination  of  the  screen  provided  the  speed  is  greater  than  a  critical 
speed  below  which  fluctuations  in  the  intensity  are  visible,  it  seemed 
unnecessary  to  make  an  extended  study  of  this  effect.     It  was  desir- 
able, however,  to  check  the  conclusion  of  previous  investigators  for 
a  range  of  speed  likely  to  be  used  in  the  experiments.     Hence,  using 
successively  two  disks — the  180°  disk  and  the  60°  disk — the  speed 
of  the  disk  was  varied  from  the  "flicker"  point  to  the  maximum 
speed  attainable  and  no  variation  of  the  illumination  within  the 
range  of  experimental  error  was  detected.    Subsequently,  therefore,  no 
attention  was  paid  to  the  speed  of  the  disk  except  to  be  sure  that  the 
speed  was  sufficiently  high,  i.  e.,  that  the  number  of  alternations  of  the 
sectors  was  sufficiently  great  to  prevent  the  possibility  of  a  "flicker." 

(b)  Disks. — In  order  to  show  the  accuracy  of  the  mechanical  con- 
struction of  the  sectored  disks,  the  readings  on  the  30°  disk  for  the 
six  separate  sectors  and  at  different  distances  from  the  periphery  of 
the  disk  are  given  in  Table  II.     The  first  column  contains  the  dis- 
tances, expressed  in  centimeters,  from  the  periphery  of  the  disk  to 
the  point  at  which  the  measurements  were  made.     The  other  six 
columns  contain  the  readings  on  the  angular  openings  of  the  six  sec- 
tors numbered  from  I  to  VI. 

Since  the  30°  disk  contained  the  smallest  sectors  of  all  the  disks 
it  had  to  be  made  and  measured  most  carefully  of  all,  for  small 
deviations  of  the  edges  of  the  sectors  from  straight  radial  lines 
would  produce  relatively  large  errors  in  the  angular  openings.  The 
absolute  angle  need  not  be  made  to  agree  very  closely  with  the  nomi- 
nal value,  as  the  subsequent  calibration  will  give  the  true  value  of 

1 1  wish  to  express  my  indebtedness  to  my  assistants,  Mr.  F.  E.  Cady  and  Mr.  A.  H. 
Schaaf ,  for  valuable  assistance  both  in  observations  and  computations. 


Hyde.} 


The  Rotating  Sectored  Disk. 


the  opening',  but  it  is  very  necessary  that  the  edges  be  made  approxi- 
mately radial  and  quite  straight,  so  that  the  mean  of  the  seven  meas- 
urements made  every  5  mm  may  represent  the  mean  value  of  the 
opening.  It  is  seen  from  Table  II  that  the  maximum  range  of 
variation  at  different  radial  distances  for  most  of  the  sectors  is  only 

TABLE  II. 

Calibration  of  30°  Disk. 


Distance  from 
Periphery 

I 

II 

III 

IV 

V 

VI 

cm 

3.0 

5°04/48// 

5°03'46" 

5°03'02" 

5°04/45// 

5°05/28// 

5°06/24// 

3.5 

05  08 

03  54 

03  00 

04  28 

05  27 

06  22 

4.0 

05  17 

03  50 

03  12 

04  26 

05  23 

06  40 

4.5 

05  21 

03  42 

03  00 

04  20 

05  14 

06  34 

5.0 

05  06 

03  52 

02  54 

04  14 

05  28 

06  57 

5.5 

05  10 

03  51 

02  45 

04  14 

05  33 

07  10 

6.0 

05  14 

03  51 

02  54 

04  28 

05  44 

07  08 

Mean  

5  05  09 

5  03  49 

5  02  58 

5  04  25 

5  05  28 

5  06  45 

about  30"  or  i  part  in  600.  The  average  deviation  from  the  mean 
opening  would  be  well  under  i  part  in  1,000. 

As  stated  above,  the  disks  were  always  mounted  in  such  a  position 
that  the  beam  of  light  passed  through  the  calibrated  part  of  the 
sectors. 

Measurements  similar  to  those  for  the  30°  disk  were  made  on  all 
the  disks,  the  final  results  of  which  in  the  form  in  which  they  were 
used  are  given  in  Table  III.  The  first  column  contains  the  various 
disks.  The  second  column  contains  the  nominal  angles  obtained 
from  the  different  disks,  and  the  third  column  gives  the  sectors  that 
were  employed  to  obtain  these  angles.  In  the  fourth  column  are 
given  the  ratios  of  the  actual  angles  to  360?  These  ratios,  compared 
with  the  ratios  of  the  squares  of  the  distances  obtained  in  the  experi- 
ments, gave  the  errors  in  the  law. 


Bulletin  of  the  Bureau  of  Standards. 
TABLE  III. 


[  Vol.  2,  No,  i. 


Disks 

Nominal  Angles 

Sectors  Used 

Corresponding  Angles 
H-36o« 

30° 

30° 

I-VI 

0.08466 

15° 

I,  III,  V 

0.04229 

15° 

II,  IV,  VI 

0.04236 

10° 

I,  IV 

0.02822 

10° 

II,  V 

0.02821 

10° 

III,  VI 

0.02823 

60° 

60° 

I-III 

0.16914 

180° 

180° 

I-VI 

0.5012 

90° 

I,  III,  V 

0.2506 

90° 

II,  IV,  VI 

0.2507 

60° 

I,  IV 

0.16697 

60° 

II,  V 

0.16718 

60° 

III,  VI 

0.16710 

210° 

210° 

I-VI 

0.5841 

240° 

240° 

I-VI 

0.6683 

120° 

I,  III,  V 

0.3341 

120° 

II,  IV,  VI 

0.3342 

270° 

270° 

I-VI 

0.7508 

90° 

I,  IV 

0.2501 

90° 

II,  V 

0.2504 

90° 

III,  VI 

0.2503 

288° 

288° 

I-VI 

0.8000 

144° 

I,  III,  V 

0.4000 

144° 

II,  IV,  VI 

0.4000 

(c)  White  Light.  —  In  order  that  the  exact  method  of  observation 
and  computation  may  be  known,  the  following  series  of  measure- 
ments of  June  2,  1905,  copied  from  the  laboratory  record  book,  is 
given: 

SERIES   XXV. 


60°  disk,  total  opening  60.89? 


—- 
300 


=  0.16914.     88-watt  Nernst 


No.  9  on  left  at  o  when  disk  is  stationary,  and  at  71.5  when  disk  is 


Hyde.} 


The  Rotating  Sectored  Disk. 


rotating.     88-watt  Nernst  No.  10  on  right,  as  comparison  lamp,  at 
fixed  distance  119.9  cm  fr°m  photometer  screen. 


60°  disk  stationary. 

Volt. 


Nernst  No.  9  at  o. 

Volt. 


122.97 

.82 

.56 

No.  10=111.01 
122.78                °'    9—  II7-° 

122.97 

•63 

.80 

122.80 

No.  10=110.99 
No.    9=117.08 

•  75 

(  —  ) 

Volt. 

(  —  ) 

Volt. 

122.33 
.07 

No.  10=110.98 
122.19             No.   9=117.08 

122.03 
1.98 

121.99 

No.  10=111.00 
No.    9=117.07 

•  17 

1.97 

60°  disk  rotating. 

Nernst  No.  9 

at  71.5. 

(  —  ) 

Volt. 

(~  ) 

Volt. 

121.91 
.89 
.80 

No.  10=111.01 
121.87             No.  '9=117.07 

121.91 

.78 
.82 

121.84 

No.  10=111.00 
No.    9=117.07 

(  +  ) 

Volt. 

(  +  ) 

Volt. 

122.44 

.22 

•23 

No.  10=111.00 

,-             No.    9=117.07 
122.26 

122.38 
.16 
•17 

122.24 

No.  10=110.99 
No.    9=117.04 

•17 

60°  disk  stationary. 

Nernst  No. 

9  at  o. 

(  +  ) 

Volt. 

(  +  ) 

Volt. 

122.  6l 
.67 
.80 

No.  10=111.00 
122.69             No.    9=117.03 

122.97 
•71 
•99 

122.85 

No.  10=110.99 
No.    9=117.06 

•73 

(-) 

Volt. 

(-) 

Volt. 

122.33 
2.10 
1.94 

No.  10=110.98 

I22.II                  N0"     9  =  117-02 

122.02 

•13 
.02 

122.06 

No.  10=110.97 
No.    9=117.03 

2.O7 

60°  disk  rotating. 

Nernst  No.  9 

at  71.5. 

(_) 

Volt. 

(_) 

Volt. 

121.77 
.87 
.82 

No.  10=110.99 
121.82             No.    9=117.04 

121.89 
.87 
.80 

121.85 

No.  10=110.99 
No.    9=117.04 

(  +  ) 

Volt. 

(  +  ) 

Volt. 

122.31 

•37 

No.  10=110.99 
122.30             No.    9=117.04 

122.20 
•31 

122.24 

No.  10=110.98 
No.    9=117.05 

.22 

.21 

60°  disk  stationary. 

Nernst  No.  9  at  o. 

(+) 

Volt. 

(  +  ) 

Volt. 

122.73 
.81 

•97 

No.  10=110.98 
122.81             Na    9=117-02 

122.83 
.64 

•57 

122.68 

No.  10=111.00 
No.    9=117.01 

.72 

26 


Bulletin  of  the  Bureau  of  Standards.  {voi.2<No.i. 


60°  disk  stationary. 

(-)  Volt. 

122.01  No.  10=110.99 

2.29  No.    9=117.02 

1.88     121.99 
1.87 
1.89 

COMPUTATIONS. 
Disk  stationary. 


Nernst  No.  9  at  o. 

(  —  )  Volt. 

121.97  No.  10=111.01 

No.    9=117.02 


i-77 
1.93 


<+)I22io  '-79 


,22.69 


,22.09 


,22.08 


,22.74 


(-)  121-99     I2I    6 
.92 


122.44 


122.42 


122.35 


9 
Disk  rotating. 

'"      ,22.25 


122.06 


(  +  )  122.30 
(-»";g 


I22.06 


,2,34 


Mean  stationary  setting 122. 40        Mean  rotating  setting 122.  06 

Position  of  Nernst  carriage o.  oo         Position  of  Nernst  carriage 71.  50 


Distance=  ..............   122.  40 

Correction  to  bar  ..............    —  o.  41 


Distance=  ..............     50.  56 

Correction  to  bar  ..............    —  o.  32 


Corrected  distance=  .....    121.  99 


Corrected  distance=  .....     50.  24 


60.89°    _o.  16914 
360°  +47=4-0.28%.     Deviation  from  Talbot's  law. 

This  method  of  observation  and  computation  was  followed 
throughout  the  investigation.  A  great  number  of  different  Nernst 
glowers,  both  of  the  88-watt  type  and  of  the  44-watt  type,  were  used. 
The  choice  between  an  88-watt  glower  and  a  44-watt  glower  for  the 
comparison  lamp  was  determined  by  convenience.  For  the  test 
lamp,  however,  measurements  were  made  with  both  types  with  the 
larger  angular  openings  in  order  to  test  the  effect  of  change  in  the 
absolute  illumination  of  the  screen.  Thus  with  the  288°,  270°, 
240°,  and  1  80°  disks  measurements  were  made  with  both  the  44- 


Hyde: 


The  Rotating  Sectored  Disk, 


27 


watt  and  the  88-watt  glowers,  each  at  two  different  distances,  so  that 
the  extreme  illuminations  used  were  in  the  ratio  of  1:4.  With  the 
60°  disk  illuminations  in  the  ratio  of  1:2  were  used,  but  in  no  case 
was  there  any  evidence  of  an  effect  due  to  absolute  intensity  of  illu- 
mination. These  variations  in  the  intensity  of  illumination  were 
not  very  large,  so  that  it  would  be  interesting  to  study  the  effect  of 
large  changes  in  the  intensity  of  illumination,  particularly  for  disks 
with  small  openings.  In  my  observations  with  openings  smaller 
than  60°  88-watt  glowers  were  always  used,  since  even  with  them 
the  illumination  of  the  photometer  screen  was  quite  small,  because 
of  the  necessarily  long  distance.  Thus  with  the  10°  opening  the 
distance  between  the  test  Nernst  and  the  screen  was  approximately 
300  cm  when  the  disk  was  unmounted  and  only  50  cm  when  the 
disk  was  rotating.  Moreover,  because  of  this  great  range  of  distance 
but  one  distance  for  each  position  could  be  used  conveniently. 


Vo  DEVIATION  FROM 
TALBOT'S  LAW 

+  0.4°/o 

-0- 

tO.  2% 

^^' 

_O_ 

C 

1 

O 

±0.0% 

300 

240 

180f 

,.-^ 

....  ^ 
^^_^^— 

'^-  ~ 
120 

) 

80 

0 

-0.2% 

O— 

TO 

FAL  AN( 

SULAR 

3PENINC 

IN    DE 

3REES 

-0.4% 

Fig.  11. — Deviation  from  Talbot's  Law. 

The  results  obtained  with  the  various  angular  openings  are  shown 
in  Table  IV,  in  which  (+)  means  that  the  disk  apparently  let 
through  more  light  than  would  be  expected  from  Talbot's  law.  It 
should  be  stated  that  the  order  in  which  the  disks  were  used  was 
most  irregular.  Several  of  them,  for  example,  were  tested  both 
near  the  beginning  and  near  the  end  of  the  investigation,  which 
extended  over  a  period  of  ten  or  twelve  months. 

The  mean  values  for  the  different  angular  openings  are  plotted 
in  the  form  of  a  curve  in  Fig.  n,  in  which  abscissas  are  angular 
openings,  and  ordinates  are  percentage  deviations  from  the  law  of 
Talbot.  The  dotted  curve  represents  the  values  given  in  Table  IV. 

It  is  seen  that  for  all  angular  openings  from  288°  to  10°  the  law 
is  verified  to  within  0.5  per  cent.  Attention  should  be  called,  how- 
ever, to  the  form  of  the  curve.  Since  the  average  deviation  of  the 
readings  for  any  one  angle  was  in  no  case  as  large  as  0.2  per  cent, 


28 


Bulletin  of  the  Bureau  of  Standards. 


[  Vol.  2,  No.  i. 


the  probable  errors  of  the  measurements  are  in  all  cases  under  o.i 
per  cent,  while  the  observed  errors  in  the  law  are  as  large  as  0.4  per 
cent.  Because  the  probable  errors  are  less  than  o.  i  per  cent,  it  does 
not  necessarily  follow,  however,  that  the  results  are  correct  to  the 

TABLE  IV. 

Percentage  Deviations  from  Talbot's  Law  Using  White  Light. 


Total  Angular  Open- 

288° 

270° 

240° 

210° 

188° 

144° 

-0.16% 

-0.05% 

-0.05% 

-0.06% 

+0.10% 

+0.24% 

+   .01 

.03 

-   .12 

-   .05 

+  -14 

.25 

-  .09 

.06 

-  .17 

-  .15 

.09 

-   .12 

.16 

+   .01 

-  .10 

+   .13 

+   -11 

Means                     

—0.09 

—0.08 

—0.08 

—0.06 

+0.04 

+0.19 

Average  variation 
from  the  mean.. 

±0.05 

zh   .04 

±   .06 

±   .00 

±   .11 

=h  .07 

Table  IV,  continued. 


Total  Angular  Open- 
ings   

120° 

90° 

60° 

30° 

15° 

10° 

+0.22% 

+0.37% 

+0.54% 

+0.35% 

+0.38% 

+0.14% 

.04 

.51 

.15 

.37 

.63 

.52 

.39 

.20 

.39 

.52 

.38 

.33 

.20 

.55 

.61 

.40 

.20 

.61 

.39 

.45 

.28 

.26 

.03 

.65 

.26 

.41 

.44 

.40 

Means  

+0.13 

+0.36 

+0.33 

+0.37 

+0.45 

+0.41 

Average  variation 
from  the  mean.. 

zb  .09 

±  .09 

±  .16 

zt   .01 

±  .13 

zb   .13 

same  accuracy.  Some  constant  source  of  error  might  possibly  be 
present.  It  will  be  noticed  from  the  table  that  approximately  the 
same  deviation  was  found  for  all  the  openings  less  than  120?  Now, 
in  all  the  measurements  on  these  angles,  the  rotating  readings  were 


Hyde.]  The  Rotating  Sectored  Disk.  29 

taken  with  the  test  Nernst  about  50  cm  from  the  photometer  screen, 
at  which  distance  the  entire  system  was  very  much  congested. 
Hence,  it  seemed  possible  that  some  stray  light  might  have  pene- 
trated to  the  screen  which  would  not  have  reached  the  screen  when 
a  longer  distance  was  used  as  in  the  stationary  readings.  In  par- 
ticular the  photometer  screen  itself  reflects  light  back  on  the  dia- 
phragms and  on  the  solid  sectors  of  the  disk,  and  since  these  were 
necessarily  very  close  to  the  screen  when  the  test  Nernst  was  only 
50  cm  away,  the  apparent  deviation  from  the  law  might  possibly  be 
due  in  part  to  this  stray  light. 

An  attempt  was  made  to  measure  the  effect  of  this  stray  light  by 
cutting  off  the  direct  rays  from  the  Nernst,  but  it  was  found  very 
difficult  to  reproduce  the  conditions,  and  so  this  method  of  attack 
was  abandoned.  A  second  method  which  seemed  productive  of 
results,  but  which  could  not  be  carried  as  far  as  desired  for  want  of 
time,  consisted  in  using  longer  distances  for  the  90°  disk  and  in 
comparing  the  15°  disk  with  the  180°  disk,  which  has  an  error  of 
+  0.04  per  cent.  Only  a  few  observations  were  made,  but  they 
seemed  to  be  in  the  right  direction.  Thus,  with  the  90°  disk  four 
determinations  at  a  much  greater  distance  than  that  used  before 
gave  as  the  errors  +0.38  per  cent,  +0.14  per  cent,  0.09  per  cent, 
and  +0.18  per  cent,  with  a  mean  of  +°-2O  per  cent,  as  against 
+  0.36  per  cent  in  the  previous  determinations.  Similarly  two 
measurements  of  the  15°  disk  against  the  180°  disk,  the  shortest 
distance  between  the  test  Nernst  and  the  photometer  screen  being 
about  73  cm  instead  of  50  cm,  as  was  used  in  the  previous  measure- 
ments, gave  as  the  errors  +0.22  per  cent  and  +0.49  per  cent,  with  a 
mean  of  +0.36  per  cent.  This  is  only  0.09  per  cent  lower  than  the 
mean  value  of  the  previous  determinations,  but  it  is  in  the  right 
direction. 

If,  now,  to  the  above  considerations  we  add  that  of  the  deviations 
of  the  radiation  of  a  cylinder  from  the  inverse  square  law,  which  are 
also  in  the  right  direction,  we  reduce  the  error  for  the  small  open- 
ings still  further.  For  a  cylinder  20  mm  long  and  i  mm  radius  the 
error  for  the  distances  used  with  the  10°  disk  would  be  +0.11  per 
cent.  For  an  88  watt  Nernst  15  mm  long  and  0.6  mm  radius  the 
error  probably  would  be  but  slightly  less  than  +  o.  1 1  per  cent,  or 
about  +0.08  per  cenj-  or  _|_O.O9  per  cent.  Similar  errors  would  be 


30  Bulletin  of  the  Bureau  of  Standards.  \_voi.  z,  NO.  i. 

present  in  the  measurements  of  the  other  disks,  so  that  the  complete 
curve  of  Fig.  1 1  would  be  lowered  by  a  small  amount,  the  lowering 
being  greatest  at  10°  where  it  would  amount  to  about  0.08  per  cent, 
and  least  at  288°,  where  it  would  be  approximately  zero. 

This  lowering  of  the  curve  due  to  the  deviation  from  the  inverse 
square  law  combined  with  that  indicated  by  the  experiments  described 
just  above  would  seem  to  justify  a  total  lowering  of  the  curve  suffi- 
cient to  bring  it  within  the  limits  +0.3  per  cent  and  —0.3  per  cent 
as  shown  in  the  solid  curve  of  Fig.  n. 

No  attempt  has  been  made  to  investigate  the  effect  of  diffraction 
at  the  edges  of  the  disk.  This  might  possibly  affect  the  result  to 
some  small  extent. 

In  order  to  determine  whether  the  personal  equation  entered  to 
any  extent  into  the  results  obtained,  several  sets  of  readings  were 
made  by  a  second  observer.  With  the  210°  disk  he  made  but  one 
set  of  measurements  obtaining  the  result  +0.04  per  cent.  With  the 
144°  opening  he  obtained  +0.21  per  cent;  with  the  120°  opening, 
+  0.16  per  cent  and  -|-o.2o  per  cent;  with  the  90°  opening,  -(-0.12 
per  cent,  +0.26  per  cent,  and  —0.12  per  cent;  with  the  60°  opening 
+  0.14  per  cent;  and  with  the  15°  opening  -j-o.n  per  cent,  +0.29 
per  cent,  +0.33  per  cent,  and  +0.37  per  cent.  His  readings  are 
thus  in  the  same  direction  as  my  own  and  for  the  most  part  agree 
with  them,  although  on  the  whole  they  show  somewhat  smaller 
deviations,  particularly  for  the  smaller  openings. 

(d)  Colored  Light. — In  the  investigation  of  the  law  with  colored 
light  it  was  thought  sufficient  to  determine  whether  for  several 
points  on  the  curve  the  values  obtained  with  colored  light  are  in 
approximate  agreement  with  the  corresponding  values  for  white 
light.  The  same  method  of  observation  as  that  for  white  light  was 
used,  but  the  error  of  observation  was  very  much  larger,  partly 
because  of  the  color  and  partly  because  of  the  reduced  intensity 
which  made  observations  on  the  15°  disk  very  difficult.  The  240°, 
60°,  and  15°  openings  were  used,  and  each  was  tested  with  red, 
green,  and  blue  light  by  inserting  pieces  of  glass  in  the  eyepiece  of 
the  photometer.  The  red  glass  was  ordinary  ruby  glass  and  was 
found  on  examination  with  a  spectroscope  to  transmit  very  little 
other  than  red,  although  the  band  in  the  red  was  quite  broad.  The 
green  glass  was  supposed  to  be  a  very  high  grade  of  monochromatic 


Hyde.} 


The  Rotating  Sectored  Disk. 


31 


glass,  but  it  transmitted  much  light  of  other  colors,  as  did  also  the 
cobalt  blue  glass  used  for  the  blue. 

In  connection  with  the  measurements  with  colored  light  it  was 
thought  desirable  to  make  a  few  experiments  with  color  differences 
on  the  two  sides  of  the  screen  as  this  condition  always  existed  in 
Ferry's  experiments  when  he  obtained  the  large  errors.  The  test 
lamp,  as  in  the  previous  experiments,  was  a  Nernst  glower  at  normal 
current.  The  comparison  lamp,  however,  was  a  16  cp  anchored 
oval,  118  volt,  3.5  watt  per  candle  incandescent  lamp  burning  at 
different  voltages  ranging  from  116  to  102  volts.  The  color  differ- 
ence was  very  marked  when  the  incandescent  lamp  was  at  normal 
voltage,  but  in  order  to  insure  the  detection  of  any  error  that  might 
exist,  the  incandescent  lamp  was  burned  at  102  volts  in  the  measure- 
ments with  the  15°  disk.  At  this  voltage  the  contrast  in  color  was 
very  great  and  yet  no  greater  deviations  than  those  for  white  light 
on  both  sides  of  the  screen  were  detected. 

TABLE  V. 

Deviations  from  Talbofs  Law  Using  Red,  Green,  and  Blue  Light,  and  Color  Difference. 


340° 

Means 

60° 

Means 

15° 

Means 

Red  light  

+0.09% 

+0.01  % 

+0.37%. 

+0.62% 

+  1.06% 

+0.44  % 

-   .07 

.86 

-  .25 

+  .52 

*+0.58 

Green  light  

—0.09 

—0.02 

+0.51 

+0.47 

+0.05 

+0.24 

+0.06 

.43 

.42 

Blue  light  

+0.01 

—0.06 

+0.41 

+0.38 

+0.30 

+0.50 

-   .13 

.35 

.70 

*+0.47 

Color  difference.  .  . 

+0.21 

+0.04 

+0.63 

+0.46 

+0.57 

+0.56 

—0.14 

.45 

.56 

.30 

In  making  the  measurements  with  color  difference  the  absorption 
strips  were  removed  from  the  Lummer-Brodhun  photometer  and  the 
setting  was  made  for  a  match,  instead  of  for  equal  contrast.  The 
same  openings  were  used  as  in  the  experiment  with  the  red,  green, 

24353— No- 


32  Bulletin  of  the  Bureau  of  Standards.          \V<>i.  2,  NO.  /.] 

and  blue  light.  All  of  the  results  of  the  experiments  with  colored 
lights,  and  of  those  in  which  there  was  a  color  difference  on  the  two 
sides  of  the  screen  are  contained  in  Table  V.  The  first  column  con- 
tains the  four  different  conditions  under  which  the  experiments 
were  made.  In  the  second,  fourth,  and  sixth  columns  are  given  the 
corresponding  results,  and  in  the  third,  fifth,  and  seventh  columns 
are  given  the  means  of  the  values  in  the  second,  fourth,  and  sixth 
columns,  respectively.  The  observations  marked  with  an  asterisk 
were  made  by  the  second  observer  and  are  not  included  in  the 
means. 

From  a  comparison  of  Tables  IV  and  V  it  is  seen  that  within 
the  range  of  experimental  error  the  deviations  from  Talbot's  law  are 
the  same  for  white  and  colored  light  and  for  difference  in  color 
on  the  two  sides  of  the  screen.  It  would  be  well,  however,  to  make 
further  experiments  on  colored  light  in  order  to  reduce  the  probable 
error,  and  obtain  results  more  nearly  comparable  with  the  results 
for  white  light. 

5.  CONCLUSIONS. 

The  results  of  this  investigation  may  be  summarized  as  follows: 

(1)  Talbot's  law,  in  its  application  to  a  rotating  sectored  disk,  is 
verified  for  white  light  for  all  total  angular  openings  between  288° 
and  10°,  to  within  a  possible  error  of  0.3  per  cent,  which  probably 
expresses  the  limit  of  accuracy  of  the  experiments. 

(2)  The  observed  deviations  from  the  law  for  red,  green,  and  blue 
light  are  of  the  same  order  of  magnitude  as  those  for  white  light, 
and  hence  Talbot's  law  is  verified  for  red,  green,  and  blue  light, 
though  not  to  such  a  high  accuracy  as  for  white  light.     Moreover, 
a  difference  in  color  on  the  two  sides  of  the  photometer  screen  pro- 
duces no  appreciable  change  in  the  observed  deviation  from  the  law. 


VITA. 

Edward  Pechin  Hyde  was  born  in  Baltimore  County,  Mary- 
land, January  3,  1879.  ^s  parents  were  Edward  I.  and  Caro- 
line R.  (Clemm)  Hyde.  He  received  his  preparatory  training 
in  the  public  schools  of  Baltimore,  Maryland,  and  entered  the 
collegiate  department  of  the  Johns  Hopkins  University  in  1897. 
He  was  graduated  from  that  institution  in  1900  with  the  degree 
of  Bachelor  of  Arts. 

In  the  following  autumn  he  entered  upon  graduate  work 
in  the  Johns  Hopkins  University,  with  physics  as  his  principal 
subject  and  mathematics  and  physical  chemistry  as  his  subordi- 
nate subjects.  He  was  appointed  to  a  Fellowship  in  1901.  In 
1902  he  entered  the  Bureau  of  Standards,  Washington,  with 
which  institution  he  is  still  connected  as  Assistant  Physicist. 
In  May,  1904,  he  married  Miss  Virginia  Getzendanner,  of  Balti- 
more, Maryland. 

In  the  progress  of  his  graduate  work  he  has  attended  lec- 
tures given  by  Prof.  J.  S.  Ames,  Prof.  R.  W.  Wood,  Prof.  F.  Mor- 
ley,  Prof.  H.  C.  Jones,  Dr.  J.  B.  Whitehead  and  Dr.  A.  Cohen. 

The  investigation  leading  to  his  dissertation  on  "Talbot's 
Law  as  Applied  to  the  Rotating  Sectored  Disk,"  was  carried 
out  in  the  photometric  laboratory  of  the  Bureau  of  Standards. 
He  desires  to  express  here  his  indebtedness  to  Prof.  S.  W. 
Stratton,  Director  of  the  Bureau  of  Standards,  for  the  courtesy 
shown  him  in  granting  him  permission  to  submit  this  investiga- 
tion as  a  dissertation  to  the  Board  of  University  Studies  of  the 
Johns  Hopkins  University,  and  to  Prof.  J.  S.  Ames,  under  whose 
general  direction  as  Director  of  the  Physical  Laboratory  of  the 
Johns  Hopkins  University  the  investigation  was  carried  out,  for 
his  interest  and  kindness  during  the  progress  of  the  work. 


O.-  THE 

[   UNIVERSITY 

OF 


